lasq1(3)

💅 NAME 💅

Welcome to the lasq1(3) page from the Library Functions Manual, bestie — this is the tea on lasq1, aka the dqds step. It's giving LAPACK bidiagonal SVD energy, and there are two Fortran subroutines to meet: dlasq1 and slasq1. No cap. 💖

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✨ SYNOPSIS ✨

🎀 Functions 🎀

• subroutine dlasq1 (n, d, e, work, info) — DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.
• subroutine slasq1 (n, d, e, work, info) — SLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.

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🫶 DETAILED DESCRIPTION 🫶

This is where the full function documentation lives, so consider this the runway to the detailed subroutine section below. Scroll, queen. 👑

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💅 FUNCTION DOCUMENTATION 💅

🧚 subroutine dlasq1

subroutine dlasq1 (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( * ) work, integer info)

DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.

💖 Purpose 💖

Okay so DLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E. The singular values are computed to high relative accuracy, in the absence of denormalization, underflow and overflow. The algorithm was first presented in by K. V. Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, 1994, and the present implementation is described in , LAPACK Working Note.

🌸 Parameters 🌸

• N — N is INTEGER. The number of rows and columns in the matrix. N >= 0.
• D — D is DOUBLE PRECISION array, dimension (N). On entry, D contains the diagonal elements of the bidiagonal matrix whose SVD is desired. On normal exit, D contains the singular values in decreasing order.
• E — E is DOUBLE PRECISION array, dimension (N). On entry, elements E(1:N-1) contain the off-diagonal elements of the bidiagonal matrix whose SVD is desired. On exit, E is overwritten.
• WORK — WORK is DOUBLE PRECISION array, dimension (4*N).
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: the algorithm failed
    • = 1, a split was marked by a positive value in E
    • = 2, current block of Z not diagonalized after 100*N iterations (in inner while loop) On exit D and E represent a matrix with the same singular values which the calling subroutine could use to finish the computation, or even feed back into DLASQ1
    • = 3, termination criterion of outer while loop not met (program created more than N unreduced blocks)

✨ Author ✨

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 107 of file dlasq1.f.

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🧚 subroutine slasq1

subroutine slasq1 (integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) work, integer info)

SLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.

💖 Purpose 💖

SLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E. The singular values are computed to high relative accuracy, in the absence of denormalization, underflow and overflow. The algorithm was first presented in by K. V. Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, 1994, and the present implementation is described in , LAPACK Working Note.

🌸 Parameters 🌸

• N — N is INTEGER. The number of rows and columns in the matrix. N >= 0.
• D — D is REAL array, dimension (N). On entry, D contains the diagonal elements of the bidiagonal matrix whose SVD is desired. On normal exit, D contains the singular values in decreasing order.
• E — E is REAL array, dimension (N). On entry, elements E(1:N-1) contain the off-diagonal elements of the bidiagonal matrix whose SVD is desired. On exit, E is overwritten.
• WORK — WORK is REAL array, dimension (4*N).
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: the algorithm failed
    • = 1, a split was marked by a positive value in E
    • = 2, current block of Z not diagonalized after 100*N iterations (in inner while loop) On exit D and E represent a matrix with the same singular values which the calling subroutine could use to finish the computation, or even feed back into SLASQ1
    • = 3, termination criterion of outer while loop not met (program created more than N unreduced blocks)

✨ Author ✨

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 107 of file slasq1.f.

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🌈 AUTHOR 🌈

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